Theory of two-component irreversible adsorption with pore diffusion control

Abstract

• Theory of pore-diffusion controlled multi-component irreversible adsorption. • Shrinking core model for multi-component irreversible binding. • Closed-form expressions for batch uptake and column breakthrough. • Solutions validated by numerical simulation with the general rate model. This paper provides a theoretical analysis of the kinetics of two-component irreversible adsorption in porous spherical particles for conditions where pore diffusion is limiting. The two components are assumed to have the same binding capacity without the possibility of displacement of one component by the other but with different effective pore diffusivities. As a result, the amounts of each component adsorbed depend on the relative rates of mass transfer within the particles. Closed-form analytical expressions derived by solving the relevant conservation equations are obtained to describe adsorption from an infinite bath with constant concentrations at the particle surface, batch adsorption in a finite bath, and adsorption in packed columns, both under constant pattern and non-constant pattern conditions. In each case, the expression derived reduces to a single integral. These expressions are in good agreement with the numerical solutions of the corresponding general rate model for conditions where the kinetics of binding is fast and provide a simple means to predict two-component adsorption in many practical cases where strong adsorption conditions prevail. Generalizations to systems with more than two components, to cases where the external mass transfer resistance is important, and to unequal capacities are also provided.